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The midpoint is the point (x, y) that is in the middle. We can find the midpoint using the midpoint formula: or you can just take the average of both the x- and y-coordinates you'll add the x-coordinates, then divide by twothen add the y-coordinates and divide by two m = ( x1 + x2 2 , y1+ y2 2 ) Examples: 1) 2) A (3, -9) B (-3, 5) A(1, 0.8) B (6, 4) x-coord = 1 + 6 x-coord = 3 + (-3) x = 0 M = (3.5, 2.4) 2 = 0 M = (0, -2) 2 2 y-coord = -9 + 5 y-coord = 0.8 + 4 y = -4 2 = -2 2 2 Now it's your turn. Make sure you write your answers as integers or decimals.... Make sure you include the parentheses ( ) when writingordered pairs: Ex: (5,2) (Some problems already have the parentheses) Make sure when writing numbers between 0 and 1, you begin with 0: Ex 1/2 = 0.5 Use no spaces between coordinates No fractions! Find the midpoint ofsegment AB. M = ( *Write as decimals, if necessary. , ) A (1, -2) (5, 1) B midpoint coordinates = *Write as an ordered pair with NO spaces. ex: (0,0) 2) Find the coordinates of the midpoint of segment AB. A (-2, 3) (2, 7) B (0.5, -0.5) (1, -1) (-1, 1) (-0.5, 0.5) What is the midpoint? A B *Write as an ordered pair with NO spaces. Use decimals if needed. ex: (5,2.5) Coordinates of midpoint = 4) Given the coordinates for segment CD, C = (-1, 6) and D = (4, 10). Find the coordinates of the midpoint of CD. 5) You can find the midpoint of every line. (read carefully!) True False Depends on the line. 6) The _________ of a segment is the point that divides the segment into two congruent segments. segment addition postulate line distance midpoint What is the midpoint of Segment AB? *Write as an ordered pair with NO spaces. Use decimals if needed. ex: (5,2.5) A B So, we will add these numbers to the midpoint to find D. So, let's look at this... If the midpoint M of segment CD is (3, 2) and C is (-2, 5) then we just need to find the difference between the x-coordinates and the y-coordinates. To find an endpoint, we will look at this without using a formula. C(-2, 5) D (3 + 5, 2 + (-3)) +5 M(3, 2) Final Answer: D(8, -1) C(-2, 5) -3 M(3, 2) 8) Use the given endpoint R and midpoint M of segmentRS to find the coordinates of the other endpoint S. R(3,0), M(0,5) Coordinates of point S: *Write as an ordered pair with NO spaces. Use decimals if needed. ex: (5,2.5) 9) In the diagram, M is the midpoint of the segment.Find AM. A AM= x+7 M 2x C 0 2 -2 4 -4 6 -6 8 -8 (it's a single number, no ordered pair) Find the midpoint A M = B 0 2 -2 4 -4 6 -6 8 -8 If M is the midpoint of Segment AB, then what is the coordinate of B? B = A M What is the midpoint of Segment XY? X (5, 12) Y (9, -2) (14, 10) (4, 10) (4, 14) (7, 5) Left Over A (4, 5) B (1, -11) Match up the midpoints with their endpoints. (2.5, -3) ? (4, 2) ? A (-2, 8)B (-6, 3) (-4, 5.5) ? A (-10, 0)B (6, -5) (-2, -2.5) ? (5, 1) ? A (7, 4)B (3, -2) What are the coordinates of the endpoint T for the Segment AT? M is the midpoint of each. A(5, -4) and M(1, 2) A(-1, 8) and M (2, 6) A(-4, 0) and M(-7, 2) A(9, 7) and M(2, 3) A(-7, -2) and M(-8, 3) T(-3, 8) ? T(5,4) ? T(-9, 8) ? T(-5, -1) ? T(-10,4) ? If M is = 3 and Segment AM = 5, what are the possiblecoordinates of A? Select all that apply 8 -8 -2 cannot be determined If R = 6 and the midpoint M is = 4, what is the coordinate of the other endpoint? |